Prediction and Inference with Missing Data in Patient Alert Systems

We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-ICU patients using ∼100 variables (vitals, lab results, assessments,…). There are several missing predictor values for most patients, which in the health sciences is the norm, rather than the exception. A Bayesian approach is presented that addresses many of the shortcomings to standard approaches to missing predictors: (i) treatment of the uncertainty due to imputation is straight-forward in the Bayesian paradigm, (ii) the predictor distribution is flexibly modeled as an infinite normal mixture with latent variables to explicitly account for discrete predictors (i.e., as in multivariate probit regression models), and (iii) certain missing not at random situations can be handled effectively by allowing the indicator of missingness into the predictor distribution only to inform the distribution of the missing variables. The proposed approach also has the benefit of providing a distribution for the prediction, including the uncertainty inherent in the imputation. Therefore, we can ask questions such as: is it possible this individual is at high risk but we are missing too much information to know for sure? How much would we reduce the uncertainty in our risk prediction by obtaining a particular missing value? This approach is applied to the BPR problem resulting in excellent predictive capability to identify deteriorating patients.

本研究详述床边患者救援（Bedside Patient Rescue, BPR）项目，该项目旨在利用约100项变量（包括生命体征、实验室检测结果、临床评估指标等）对非重症监护室（non-ICU）患者的不良事件开展风险预测。多数患者存在多项缺失的预测变量值，这在健康科学领域属于普遍常态，而非罕见特例。针对缺失预测变量的标准处理方法存在诸多缺陷，本研究提出一种贝叶斯方法（Bayesian approach）以解决上述问题：（1）在贝叶斯范式中，对缺失值插补带来的不确定性进行处理直观简便；（2）通过结合隐变量的无限正态混合模型对预测变量分布进行灵活建模，可显式处理离散型预测变量（如多变量概率单位回归模型中的处理逻辑）；（3）通过将缺失标识纳入预测变量分布以辅助缺失变量的分布推断，可有效处理部分非随机缺失（missing not at random, MNAR）场景。所提方法还可输出预测结果的分布，涵盖插补过程中固有的不确定性。据此可开展如下问题探究：例如，某患者是否确实处于高风险状态，但因缺失过多信息而无法确切判定？若获取某一特定缺失变量的值，可在多大程度上降低风险预测中的不确定性？将该方法应用于BPR项目相关问题后，其在识别病情恶化患者方面展现出优异的预测性能。